This paper determines the wavenumber surface describing the production of sound when convected vorticity strikes the leading edge of an aircraft wing or fan blade. The acoustic part of the wavenumber surface consists of four sheets, namely an ellipsoid, half an elliptic cylinder, and two parallel planes. The half-cylinder, which has two infinite straight edges, is wrapped around the ellipsoid, i.e. is tangential to it along a half-ellipse. Each of the parallel planes contains an edge of the half-cylinder, and is tangential both to the half-cylinder and the ellipsoid; and each plane contains a special point at which there is a triple tangency of the plane, the half-cylinder, and the ellipsoid. The wavenumber surface also contains a fifth sheet, describing convection of vorticity with the mean flow; this sheet is a plane, perpendicular to the two acoustic planes. The for acoustic sheets determine the asymptotic properties of the radiated sound field; in particular the half-ellipse, two straight edges, and two triple points determine the special functions describing the sound radiated in certain special directions. The author believes that the wavenumber surface has not previously been determined for a diffraction problem. Intriguingly, the knife-edge in physical space leads to knife-edges in wavenumber space, a result which can be expected in general. The method in the paper for determining the wavenumber surface applies to any half-plane diffraction problem, e.g. the scattering of sound by a half-plane, the scattering of an elastic wave by a crack, or the scattering of Rossby wave by a vertical barrier.
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